PRIPRISSMMAANNDD

SPECIAL PRISMSPECIAL PRISM

PRIPRISSMMAANNDD

SPECIAL PRISMSPECIAL PRISM

……mmaatthheemmaattiicc pprreesseennttaattiioonn

PRISM

about prism:• 3D geometric

figure• faces, vertex,

edge = based on the type of the prism

kinds of prism: square

prism/cube rectangular

prism triangular prismetc

definition of square prism/cube

square prism/cube is a three dimensional geometric figure with all sides made of squares—called faces.

this presentation describe about cube as a prism and cylinder as a special prism, and just describe a little about rectangular prism…

…next slide will describe more about cube: side, vertex, edge, volume, surface area, and diagonal formula

C U EB

cubedescription:

3D geometric figure

all sides are same

all sides made of square—called faces

side

cube’s surface area formula

450

756

3256

356

62

2

s

26 s

35

surface area = the sum of areas of all the face =Q : find the cube surface area if

the edge isA : surface area

surface

area

cube’s volume formula

V = Volumesa = side area

s = length of edgeSa = Surface area

3

2

s

ss

hsaV

e.g:

1) V = s3 = 73 = 343 cm2

2)

1562525sV

25s

625s

625s6

3750s

6s3750

6sSa

?V

?s

3750Sa

33

2

2

2

2

volume

cube’s faces, spaces, planes diagonal

cube has 12 faces diagonal• formula : • the fact :

cube has 4 spaces diagonal• formula :

• the fact :

cube has 6 planes diagonal• formula :

• the fact :

2s2sssACABAC 22222

2s

3s

2s2

3s

3s

2ss

sss

ds

2

22

222

22

2s

2ss2

definition of rectangular prism

rectangular prism is a three dimensional figure that has two same sides and other four same sides. the figure is like cube, but

not all sides are the same.

rectangular prism’s surface area formula

Q : Sa = 426 cm2

h = 12 cmw = 9 cmt = ?

A :

twthwh2Sa

5cmt

21042t

42621t2

4269t12t1082

426t9t129122

surfacearea

rectangular prism’s volume formula

Q : V = 9000 cm3

h = 10 cm w = 15 cm t = ?

A : 9000 = 10 x 15 x t 9000 = 150 x t 150t = 9000 t = 60 cm

twhV

volume

rectangular prism’s faces, spaces, planes diagonal

to find the faces, spaces, planes diagonal for rectangular prism is same as cube. but, to find the faces and spaces for rectangular prism, find it with Pythagoras theory—because not all sides are same. this is the basic formula :

to find the planes diagonal for rectangular prism, the formula is same as to find the area of rectangle. this is the basic formula : h x w

22 bac

SPECIAL PRISM

for special prism, we will describe about cylinder—circle prism.

definition of cylinder

cylinder/circle prism is a three dimensional geometric figure that has two circle sides and a side who covers the figure around that two

circles

C y l in r

ED

cylinderdescription

3D figure

has 2 same-circle-side and one rectangular cover

has no vertex

side cover

cylinder’s surface area formula

• surface area1) cover area =

2) circle side area =

3) perfect surface area (with two circle sides) =

4) imperfect surface area (without one circle side) =

t2ππ

2πr

tr2ππ2ππr2ππ2

2trπr2ππrπr2

cylinder’s volume formula

• volume1) circle area = 2) volume = one circle side area x t = 3) d = 2r4) r = ½ d5) volume =

2πrtπr2

tπd41 2

example : volume

Q : d = 7 cmt = 14 cmV = ?

A : V =

=

=

= 462 cm3

tπd41 2

127722

41 2

12497

22

4

1

vo

lu me

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